[Book Cover]

Discrete Mathematics with Graph Theory, 1/e

Edgar G. Goodaire, Memorial Univ of Newfoundland
Michael M. Parmenter, Memorial Univ of Newfoundland

Published August, 1997 by Prentice Hall Engineering/Science/Mathematics

Copyright 1998, 527 pp.
Cloth
ISBN 0-13-602079-8


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Summary

Adopting a user-friendly, conversational—and at times humorous—style, these authors make the principles and practices of discrete mathematics as stimulating as possible while presenting comprehensive, rigorous coverage. Examples and exercises integrated throughout each chapter serve to pique student interest and bring clarity to even the most complex concepts. Above all, the book is designed to engage today's students in the interesting, applicable facets of modern mathematics.

Features


Uses topics in discrete math as a vehicle for teaching proofs, introducing the basic elements of logic and the major methods of proof by guiding readers through examples, rather than relying on truth tables.
Draws attention to the technique about to be employed before giving each proof.
Designs coverage with the inexperienced student in mind, establishing a pace that is leisurely and conversational, yet rigorous and serious about theorem proving.
Places an unusually strong emphasis on graph theory, incorporating its coverage throughout seven chapters.
Provides comprehensive coverage of number theory which concludes with a section of applications to the real world, including ISBNs, universal product codes, and cryptography.
Designs coverage to be flexible enough to suit several quite distinct types of one-semester courses.
Offers more than 180 worked examples and problems, over 1,000 exercises, and 140 Pauses—short questions inserted at strategic points throughout each discussion and designed to reinforce a particular point.

  • Provides full solutions to Pauses at the end of each section, prior to the exercise sets.
Keeps material interesting and readers alert by incorporating relevant applications and historical anecdotes throughout.


Table of Contents
    0. Yes, There Are Proofs!
    1. Sets and Relations.
    2. Functions.
    3. The Integers.
    4. Induction and Recursion.
    5. Principles of Counting.
    6. Permutations and Combinations.
    7. Algorithms.
    8. Graphs.
    9. Paths and Circuits.
    10. Applications of Paths and Circuits.
    11. Trees.
    12. Depth-First Search and Applications.
    13. Planar Graphs and Colorings.
    14. The Max Flow—Min Cut Theorem.
    Solutions to Selected Exercises.
    Glossary.
    Index.


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